Categoricity of an abstract elementary class in two successive cardinals

1998/05/15 by Shelah, Saharon
#FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.math/9805146

Abstract

We investigate categoricity of abstract elementary classes without any remnants of compactness (like non-definability of well ordering, existence of E.M. models or existence of large cardinals). We prove (assuming a weak version of GCH around lambda) that if K is categorical in lambda, lambda⁺, LS(K) <= lambda and 1 <= I(lambda⁺⁺,K)< 2^lambda⁺⁺ then K has a model in lambda⁺⁺⁺ .

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